Vortex states, in which the dipoles form a closure structure, have been discovered in small magnetic disks in the last seven years (see, e.g., Ref. [1] and references therein). Also see U.S. patent application Ser. Nos. 11/811,444; 11/151,088; 60/580,940; and 60/632,040, all of the disclosures of which are incorporated herein by reference in their entireties. Interestingly, vortex structures have also been recently predicted in another kind of dipolar system of high importance, namely ferroelectrics [2]—when these latter are of nanoscale size and under open-circuit electric boundary condition [3] (i.e., for no or small screening of the polarization-induced surface charges). The existence of these vortices holds tremendous promise for nanotechnology. However, in order to fulfill such promise, one has to solve the challenging problem of controlling the vortices' chirality. As a matter of fact, magnetic and electric vortices cannot directly couple with homogeneous magnetic and electric fields [4-7]. Alternative methods have thus been suggested for such control, ranging from simultaneously applying an electric and a magnetic field and taking advantage of their cross-product [4] to the use of inhomogeneous fields [2,6]. Unfortunately, these methods are by no means trivial. This explains why the recent observation that the chirality of vortices can be switched by applying a homogeneous magnetic field in asymmetric magnetic disks is an important breakthrough (see Ref. [1] and references therein). Moreover, this switching involves peculiar intermediate states, namely the so-called onion states, which makes it even more interesting (onion states consist of two domains with semicircular magnetizations of different helicity [8]). However, this recent observation also raises many important questions. For instance, the fundamental reason behind such switching is a mystery. Similarly, the precise role of the shape's asymmetry on that control remains unexplained. Furthermore, it is worthwhile to know if a homogeneous electric field can also affect the magnitude of electric vortices and switch their chirality in (asymmetric) ferroelectrics—which will make the control of vortices by homogeneous field a general phenomena in (asymmetric) dipolar systems. If such possibility indeed occurs, determining if onion, or even other, intermediate states are also involved in that switching is of high interest.
Fabrication of asymmetrical magnetic rings [1, 18] has been reported.